This study investigates the asymptotic performance of the quadratic discriminant function (QDF) under skewed training samples. The main objective of this study is to evaluate the performance of the QDF under skewed distribution considering different sample size ratios, varying the group centroid separators and the number of variables. Three populations [Formula: see text] with increasing group ...

In this paper we apply the structural risk minimization principle as an appropriate criterion to train decision feedback and transversal equalizers. We consider both linear discriminant (optimal hyperplane) and nonlinear discriminant (support vector machine) classi6ers as an alternative to the linear minimum mean-square error (MMSE) equalizer and radial basis function (RBF) networks, respective...

Support vector machine (SVM) is a very speci1c type of learning algorithms characterized by the capacity control of the decision function, the use of the kernel functions and the sparsity of the solution. In this paper, we investigate the predictability of 1nancial movement direction with SVM by forecasting the weekly movement direction of NIKKEI 225 index. To evaluate the forecasting ability o...

The tame kernel of the K2 of a number field F is the kernel of some explicit map K2F → ⊕ k∗ v , where the product runs over all finite primes v of F and kv is the residue class field at v. When S is a set of primes of F , containing the infinite ones, we can consider the S-unit group US of F . Then US ⊗ US has a natural image in K2F . The tame kernel is contained in this image if S contains all...

In this paper, we prove that for any positive fundamental discriminant D > 1596, there is always at least one prime p ≤ D0.45 such that the Kronecker symbol (D/p) = −1. This improves a result of Granville, Mollin and Williams, where they showed that the least inert prime p in a real quadratic field of discriminant D > 3705 is at most √ D/2. We use a “smoothed” version of the Pólya–Vinogradov in...

This paper presents a comparative case study on the classification accuracy between 5 methods for golf putting performance analysis. In a previous work, a digital camera was used to capture 30 trials of 6 expert golf players. The detection of the horizontal position of the golf club was performed using a computer vision technique followed by the estimation algorithm Darwinian Particle Swarm Opt...

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We present an algorithm for computing the class number of the quadratic number field of discriminant d. The algorithm terminates unconditionally with the correct answer and, under the GRH, executes in Oε(|d|) steps. The technique used combines algebraic methods with Burgess’ theorem on character sums to estimate L(1, χd). We give an explicit version of Burgess’ theorem valid for prime discrimin...